Upload
others
View
4
Download
0
Embed Size (px)
Citation preview
Dr. Badreddine AYADI
2016
Lubrication
and
Journal Bearings
Text Book : Mechanical Engineering Design, 9th Edition
Chapter 12
UNIVERSITY OF HAIL College of Engineering
Department of Mechanical Engineering
Chapter Outline
Introduction
Types of Lubrication
Viscosity
Petroff’s Equation
Stable Lubrication
Thick-Film Lubrication
Hydrodynamic Theory
Design Considerations
The Relations of the Variables
Slide 2 Lubrication and Journal Bearings
Introduction
Slide 3 Lubrication and Journal Bearings
The object of lubrication is to reduce friction, wear, and heating of
machine parts that move relative to each other.
A lubricant is any substance that, when inserted between the moving
surfaces, accomplishes these purposes.
In the study of lubrication and journal bearings, additional fundamental
studies, such as chemistry, fluid mechanics, thermodynamics, and heat
transfer, must be utilized in developing the material.
Types of Lubrication
Slide 4 Lubrication and Journal Bearings
Five distinct forms of lubrication may be identified:
1 Hydrodynamic
2 Hydrostatic
3 Elastohydrodynamic
4 Boundary
5 Solid film
Hydrodynamic lubrication means that:
• the load-carrying surfaces of the bearing are separated by a relatively
thick film of lubricant, so as to prevent metal-to-metal contact,
• the stability thus obtained can be explained by the laws of fluid
mechanics.
Hydrodynamic lubrication is also called full-film, or fluid, lubrication.
Slide 5 Lubrication and Journal Bearings
Types of Lubrication
Hydrostatic lubrication is obtained by introducing the lubricant, which is
sometimes air or water, into the load-bearing area at a pressure high
enough to separate the surfaces with a relatively thick film of lubricant.
So, unlike hydrodynamic lubrication, this kind of lubrication does not
require motion of one surface relative to another.
Slide 6 Lubrication and Journal Bearings
Types of Lubrication
Elastohydrodynamic lubrication is the phenomenon that occurs when a
lubricant is introduced between surfaces that are in rolling contact, such as
mating gears or rolling bearings.
Slide 7 Lubrication and Journal Bearings
Boundary lubrication happens when the highest asperities may be
separated by lubricant films only several molecular dimensions in thickness.
The reasons of this can be one of the following:
a- Insufficient surface area.
b- A drop in the velocity of the moving surface.
c- A lessening in the quantity of lubricant delivered to a bearing
d- An increase in the bearing load, or an increase in lubricant temperature
resulting in a decrease in viscosity.
Types of Lubrication
Solid film lubrication when bearings must be operated at extreme
temperatures, a solid-film lubricant such as graphite or molybdenum
disulfide must be used because the ordinary mineral oils are not
satisfactory.
Slide 8 Lubrication and Journal Bearings
Types of Lubrication
Viscosity
Slide 9 Lubrication and Journal Bearings
In Fig. 12–1 let plate A be moving with a velocity U on a film of
lubricant of thickness h. We imagine the film as composed of a series
of horizontal layers and the force F causing these layers to deform or
slide on one another just like a deck of cards.
The layers in contact with the moving plate are assumed to have a
velocity U; those in contact with the stationary surface are assumed to
have a zero velocity.
Intermediate layers have velocities that depend upon their distances y
from the stationary surface.
Slide 10 Lubrication and Journal Bearings
Viscosity
Newton’s viscous effect states that the shear stress in the fluid is
proportional to the rate of change of velocity with respect to y. Thus
where μ is the constant of proportionality and defines absolute viscosity,
also called dynamic viscosity. The derivative du/dy is the rate of change
of velocity with distance and may be called the rate of shear, or the
velocity gradient. The viscosity μ is thus a measure of the internal
frictional resistance of the fluid. For most lubricating fluids, the rate of
shear is constant, and du/dy = U/h. Thus, from Eq. (12–1),
Slide 11 Lubrication and Journal Bearings
Viscosity Fluids exhibiting this characteristic are said to be Newtonian fluids.
The absolute viscosity is measured by the pascal-second (Pa・s) in SI;
this is the same as a Newton-second per square meter.
Slide 12 Lubrication and Journal Bearings
Petroff’s Equation
The phenomenon of bearing friction was first explained by Petroff on
the assumption that the shaft is concentric.
Let us now consider a vertical shaft rotating in a guide bearing. It is
assumed that the bearing carries a very small load, that the clearance
space is completely filled with oil, and that leakage is negligible (Fig.12–3).
We denote the radius of the shaft by r,
Slide 13 Lubrication and Journal Bearings
Petroff’s Equation the radial clearance by c, and the length of the bearing by l, all
dimensions being in inches. If the shaft rotates at N rev/s, then its
surface velocity is U = 2πrN in/s. Since the shearing stress in the
lubricant is equal to the velocity gradient times the viscosity, from
Eq. (12–2) we have
where the radial clearance c has been substituted for the distance h.
The force required to shear the film is the stress times the area. The
torque is the force times the lever arm r. Thus
Slide 14 Lubrication and Journal Bearings
Petroff’s Equation
Substituting the value of the torque from Eq. (c) in Eq. (b) and solving
for the coefficient of friction, we find
If we now designate a small force on the bearing by W, in pounds-force,
then the pressure P, in pounds-force per square inch of projected area,
is P = W/ 2rl. The frictional force is f W, where f is the coefficient of
friction, and so the frictional torque is
Equation (12–6) is called Petroff’s equation and was first published
in 1883.
Slide 15 Lubrication and Journal Bearings
Petroff’s Equation
The bearing characteristic number, or the Sommerfeld number, is
defined by the equation
The Sommerfeld number is very important in lubrication analysis
because it contains many of the parameters that are specified by the
designer. Note that it is also dimensionless. The quantity r/c is called
the radial clearance ratio. If we multiply both sides of Eq. (12–6) by this
ratio, we obtain the interesting relation
Slide 16 Lubrication and Journal Bearings
Stable Lubrication
The difference between boundary and hydrodynamic lubrication can be
explained by reference to Fig. 12–4.
A design constraint to keep thick-film lubrication is to be sure that
Slide 17 Lubrication and Journal Bearings
It is also helpful to see that a small viscosity, and hence a small μN/P,
means that the lubricant film is very thin and that there will be a greater
possibility of some metal-to-metal contact, and hence of more friction.
Thus, point C represents what is probably the beginning of metal-to-
metal contact as μN/P becomes smaller.
Stable Lubrication
Slide 18 Lubrication and Journal Bearings
Thick-Film Lubrication
Let us now examine the formation of a lubricant film in a journal
bearing. Figure 12–5a shows a journal that is just beginning to rotate in
a clockwise direction. Under starting conditions, the bearing will be dry,
or at least partly dry, and hence the journal will climb or roll up the right
side of the bearing as shown in Fig. 12–5a.
Now suppose a lubricant is introduced into the top of the bearing as
shown in Fig. 12–5b.
Slide 19 Lubrication and Journal Bearings
Thick-Film Lubrication
The action of the rotating journal is to pump the lubricant around the
bearing in a clockwise direction. The lubricant is pumped into a wedge
shaped space and forces the journal over to the other side.
A minimum film thickness h0 occurs, not at the bottom of the journal,
but displaced clockwise from the bottom as in Fig. 12–5b. This is
explained by the fact that a film pressure in the converging half of the
film reaches a maximum somewhere to the left of the bearing center.
Figure 12–5 shows how to decide whether the journal, under
hydrodynamic lubrication, is eccentrically located on the right or on the
left side of the bearing. Visualize the journal beginning to rotate. Find
the side of the bearing upon which the journal tends to roll. Then, if the
lubrication is hydrodynamic, mentally place the journal on the opposite
side.
Slide 20 Lubrication and Journal Bearings
Thick-Film Lubrication
The nomenclature of a journal bearing is shown in Fig. 12–6. The
dimension c is the radial clearance and is the difference in the radii of
the bushing and journal.
Slide 21 Lubrication and Journal Bearings
Thick-Film Lubrication
In Fig. 12–6 the center of the journal is at O and the center of the bearing
at O’. The distance between these centers is the eccentricity and is
denoted by e. The minimum film thickness is designated by h0, and it
occurs at the line of centers. The film thickness at any other point is
designated by h. We also define an eccentricity ratio as
The bearing shown in the figure is known as a partial bearing. If the
radius of the bushing is the same as the radius of the journal, it is
known as a fitted bearing. If the bushing encloses the journal, as
indicated by the dashed lines, it becomes a full bearing. The angle β
describes the angular length of a partial bearing. For example, a 120◦
partial bearing has the angle β equal to 120◦.
Slide 22 Lubrication and Journal Bearings
Hydrodynamic Theory
Reynolds pictured the lubricant as adhering to both surfaces and
being pulled by the moving surface into a narrowing, wedge-shaped
space so as to create a fluid or film pressure of sufficient intensity to
support the bearing load.
The important simplifying assumptions resulted from Reynolds’
realization that the fluid films were so thin in comparison with the
bearing radius that the curvature could be neglected. This enabled him
to replace the curved partial bearing with a flat bearing, called a plane
slider bearing.
Slide 23 Lubrication and Journal Bearings
Hydrodynamic Theory
Figure 12–9a shows a journal rotating in the clockwise direction supported
by a film of lubricant of variable thickness h on a partial bearing, which is
fixed. We specify that the journal has a constant surface velocity U. Using
Reynolds’ assumption that curvature can be neglected, we fix a right-
handed xyz reference system to the stationary bearing.
Slide 24 Lubrication and Journal Bearings
Hydrodynamic Theory
Other assumptions made were:
1 The lubricant obeys Newton’s viscous effect, Eq. (12–1).
2 The forces due to the inertia of the lubricant are neglected.
3 The lubricant is assumed to be incompressible.
4 The viscosity is assumed to be constant throughout the film.
5 The pressure does not vary in the axial direction.
6 The bushing and journal extend infinitely in the z direction; this means
there can be no lubricant flow in the z direction.
7 The film pressure is constant in the y direction. Thus the pressure
depends only on the coordinate x.
8 The velocity of any particle of lubricant in the film depends only on the
coordinates x and y.
Slide 25 Lubrication and Journal Bearings
We now select an element of lubricant in the film (Fig. 12–9a) of
dimensions dx, dy, and dz, and compute the forces that act on the
sides of this element. As shown in Fig. 12–9b, normal forces, due to
the pressure, act upon the right and left sides of the element, and
shear forces, due to the viscosity and to the velocity, act upon the
top and bottom sides. Summing the forces in the x direction gives
In solving this equation and using the boundary conditions, at y = 0
the lubricant velocity u = 0 and at y = h the lubricant velocity u = U
(see Figure 12-10), Reynolds found an approximate solution is due
to Sommerfeld expressed by the form
Hydrodynamic Theory
Slide 26 Lubrication and Journal Bearings
Hydrodynamic Theory
where indicates a functional relationship. Sommerfeld found the
functions for halfbearings and full bearings by using the assumption
of no side leakage.
Slide 27 Lubrication and Journal Bearings
Design Considerations
We may distinguish between two groups of variables in the design of
sliding bearings. In the first group are those whose values either are
given or are under the control of the designer. These are:
1 The viscosity μ
2 The load per unit of projected bearing area, P
3 The speed N
4 The bearing dimensions r, c, β, and l
Of these four variables, the designer usually has no control over the
speed, because it is specified by the overall design of the machine.
Sometimes the viscosity is specified in advance, as, for example, when
the oil is stored in a sump and is used for lubricating and cooling a
variety of bearings. The remaining variables, and sometimes the
viscosity, may be controlled by the designer and are therefore the
decisions the designer makes. In other words, when these four
decisions are made, the design is complete.
Slide 28 Lubrication and Journal Bearings
Design Considerations
In the second group are the dependent variables. The designer cannot
control these except indirectly by changing one or more of the first group.
These are:
1 The coefficient of friction f
2 The temperature rise T
3 The volume flow rate of oil Q
4 The minimum film thickness h0
This group of variables tells us how well the bearing is performing, and
hence we may regard them as performance factors. Certain limitations
on their values must be imposed by the designer to ensure satisfactory
performance. These limitations are specified by the characteristics of
the bearing materials and of the lubricant. The fundamental problem in
bearing design, therefore, is to define satisfactory limits for the second
group of variables and then to decide upon values for the first group
such that these limitations are not exceeded.
Slide 29 Lubrication and Journal Bearings
Significant Angular Speed
In the next section we will examine several important charts relating
key variables to the Sommerfeld number. To this point we have
assumed that only the journal rotates and it is the journal rotational
speed that is used in the Sommerfeld number. It has been discovered
that the angular speed N that is significant to hydrodynamic film
bearing performance is
Where Nj = journal angular speed, rev/s
Nb = bearing angular speed, rev/s
Nf = load vector angular speed, rev/s
When determining the Sommerfeld number for a general bearing, use
Eq. (12–13) when entering N. Figure 12–11 shows several situations
for determining N.
Design Considerations
Slide 30 Lubrication and Journal Bearings
Design Considerations